tag:blogger.com,1999:blog-31085516.post4333001617148429780..comments2024-03-27T03:13:12.133-04:00Comments on Change of Basis: Fun with L-tilesDocTurtlehttp://www.blogger.com/profile/15154912977859107986noreply@blogger.comBlogger6125tag:blogger.com,1999:blog-31085516.post-11561922078990757612011-02-15T16:14:58.564-05:002011-02-15T16:14:58.564-05:00Only fun day? Math 280 is loads of fun! We get t...Only fun day? Math 280 is loads of fun! We get to watch Patrick kick over calc books to teach us proof by induction. Not to mention we got to use L tiles as a visual learning tool and introduction to the proof style. In fact, I feel that the way that Patrick teaches mathematical proof adds an extra layer of flavor and color to the subject that may otherwise seem dry and slightly lethargic. DON'T CHANGE ANYTHING! Maybe more mass chanting when we arrive at a contradiction, but other than that DON'T CHANGE ANYTHING!Justin O'Connornoreply@blogger.comtag:blogger.com,1999:blog-31085516.post-38797693829067511012011-02-14T08:18:46.055-05:002011-02-14T08:18:46.055-05:00@Anonymous: are you saying class isn't typical...@Anonymous: are you saying class isn't typically fun? I ask this somewhat seriously: though the primary goal of the class is not to have fun, having fun while learning certainly helps, and if there's anything I can do to make it a more relaxed and pleasant atmosphere, I hope you know that I will. Suggestions?DocTurtlehttps://www.blogger.com/profile/15154912977859107986noreply@blogger.comtag:blogger.com,1999:blog-31085516.post-86729146463474468342011-02-14T08:04:55.565-05:002011-02-14T08:04:55.565-05:00Please don't tell me this is the only fun day ...Please don't tell me this is the only fun day we will have all semester. We have another 2.5 months!Anonymousnoreply@blogger.comtag:blogger.com,1999:blog-31085516.post-43227846091257811822011-02-12T16:52:05.441-05:002011-02-12T16:52:05.441-05:00We all had so much fun with this project! Such an...We all had so much fun with this project! Such an interesting way to begin learning about one of the harder methods of mathematical proofs!Justin O'Connornoreply@blogger.comtag:blogger.com,1999:blog-31085516.post-44572787859184499572011-02-11T14:30:56.646-05:002011-02-11T14:30:56.646-05:00They're L-shaped tiles with short sides of len...They're L-shaped tiles with short sides of length 1 and long sides of length 2. This "unit" tile we call <i>L</i>1. The tile <i>Lk</i> is the shape formed by scaling this one by a factor <i>k</i>.<br /><br />You can prove through a three-case inductive argument that one can build <i>Lk</i> out of non-overlapping <i>L</i>s, for any positive integer <i>k</i>. We were constructing an intuitive skeleton for that argument.DocTurtlehttps://www.blogger.com/profile/15154912977859107986noreply@blogger.comtag:blogger.com,1999:blog-31085516.post-79089087897834188832011-02-11T14:06:19.651-05:002011-02-11T14:06:19.651-05:00Do tell a little bit about what you are doing with...Do tell a little bit about what you are doing with the L-tiles? Please?Jean Mariehttps://www.blogger.com/profile/15235914912771745222noreply@blogger.com